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  2. List of limits - Wikipedia

    en.wikipedia.org/wiki/List_of_limits

    In general, any infinite series is the limit of its partial sums. For example, an analytic function is the limit of its Taylor series, within its radius of convergence. = =. This is known as the harmonic series. [6]

  3. Limit (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Limit_(mathematics)

    In mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. [1] Limits of functions are essential to calculus and mathematical analysis , and are used to define continuity , derivatives , and integrals .

  4. Limit of a function - Wikipedia

    en.wikipedia.org/wiki/Limit_of_a_function

    The function = {< has a limit at every non-zero x-coordinate (the limit equals 1 for negative x and equals 2 for positive x). The limit at x = 0 does not exist (the left-hand limit equals 1, whereas the right-hand limit equals 2).

  5. Iterated limit - Wikipedia

    en.wikipedia.org/wiki/Iterated_limit

    In multivariable calculus, an iterated limit is a limit of a sequence or a limit of a function in the form , = (,), (,) = ((,)),or other similar forms. An iterated limit is only defined for an expression whose value depends on at least two variables. To evaluate such a limit, one takes the limiting process as one of the two variables approaches some number, getting an expression whose value ...

  6. Second partial derivative test - Wikipedia

    en.wikipedia.org/wiki/Second_partial_derivative_test

    If D(a, b) = 0 then the point (a, b) could be any of a minimum, maximum, or saddle point (that is, the test is inconclusive). Sometimes other equivalent versions of the test are used. In cases 1 and 2, the requirement that f xx f yy − f xy 2 is positive at (x, y) implies that f xx and f yy have the same sign there.

  7. List of calculus topics - Wikipedia

    en.wikipedia.org/wiki/List_of_calculus_topics

    Elementary Calculus: An Infinitesimal Approach; Nonstandard calculus; Infinitesimal; Archimedes' use of infinitesimals; For further developments: see list of real analysis topics, list of complex analysis topics, list of multivariable calculus topics

  8. Outline of calculus - Wikipedia

    en.wikipedia.org/wiki/Outline_of_calculus

    Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of contemporary mathematics education . Calculus has widespread applications in science , economics , and engineering and can solve many problems for which algebra alone is insufficient.

  9. One-sided limit - Wikipedia

    en.wikipedia.org/wiki/One-sided_limit

    The function () = + ⁡ (), where ⁡ denotes the sign function, has a left limit of , a right limit of +, and a function value of at the point =. In calculus, a one-sided limit refers to either one of the two limits of a function of a real variable as approaches a specified point either from the left or from the right.

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